quantum_theta

plasmapy.formulary.quantum.quantum_theta(T: Quantity, n_e: Quantity) Quantity[source]

Compare Fermi energy to thermal kinetic energy to check if quantum effects are important.

The quantum theta (\(θ\)) of a plasma is defined by

\[θ = \frac{E_T}{E_F}\]

where \(E_T\) is the thermal energy of the plasma and \(E_F\) is the Fermi energy of the plasma.

Parameters:
  • T (Quantity) – The temperature of the plasma.

  • n_e (Quantity) – The electron number density of the plasma.

Examples

>>> import astropy.units as u
>>> quantum_theta(1 * u.eV, 1e20 * u.m**-3)
<Quantity 127290.619...>
>>> quantum_theta(1 * u.eV, 1e16 * u.m**-3)
<Quantity 59083071...>
>>> quantum_theta(1 * u.eV, 1e26 * u.m**-3)
<Quantity 12.72906...>
>>> quantum_theta(1 * u.K, 1e26 * u.m**-3)
<Quantity 0.00109...>
Returns:

theta

Return type:

Quantity

Notes

The thermal energy of the plasma (\(E_T\)) is defined by

\[E_T = k_B T\]

where \(k_B\) is the Boltzmann constant and \(T\) is the temperature of the plasma.

See also

Fermi_energy